Problem: Solve for $x$ : $3x^2 - 48x + 189 = 0$
Solution: Dividing both sides by $3$ gives: $ x^2 {-16}x + {63} = 0 $ The coefficient on the $x$ term is $-16$ and the constant term is $63$ , so we need to find two numbers that add up to $-16$ and multiply to $63$ The two numbers $-7$ and $-9$ satisfy both conditions: $ {-7} + {-9} = {-16} $ $ {-7} \times {-9} = {63} $ $(x {-7}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -7) (x -9) = 0$ $x - 7 = 0$ or $x - 9 = 0$ Thus, $x = 7$ and $x = 9$ are the solutions.